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postnew [5]
3 years ago
12

Solve for z Please help me, thank u!!!

Mathematics
1 answer:
gizmo_the_mogwai [7]3 years ago
3 0

-3.6

Step-by-step explanation:

z/(-2) + -5 = -3.2 → times -2

z + 10 = 6.4

z = 6.4 - 10

z = -3.6

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In RST, RS = 7, RT = 10, and ST = 8. Which angle of RST has the smallest measure? A T BCANNT BE DETERMINDED C R D S
Scrat [10]

Answer:

Correct answer is option A. T

Step-by-step explanation:

Given that

In a \triangle RST, RS = 7, RT = 10, and ST = 8.

To find:

Smallest angle = ?

Solution:

We can use cosine rule here to find the angle.

Formula for cosine rule:

cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}

Where  

a is the side opposite to \angle A

b is the side opposite to \angle B

c is the side opposite to \angle C

Using the cosine rule:

cos T = \dfrac{ST^{2}+RT^{2}-RS^{2}}{2\times ST \times RT}\\\Rightarrow cos T = \dfrac{8^{2}+10^{2}-7^{2}}{2\times 8 \times 10}\\\Rightarrow cos T = \dfrac{64+100-49}{160}\\\Rightarrow cos T = \dfrac{115}{160}\\\Rightarrow \angle T = cos^{-1}(0.71875)\\\Rightarrow \angle T = 44.05^\circ

Now, let us use Sine rule to find other angles:

\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}

\dfrac{RS}{sinT} = \dfrac{ST}{sinR} = \dfrac{RT}{sinS}\\\Rightarrow \dfrac{7}{sin44.05} = \dfrac{8}{sinR} = \dfrac{10}{sinS}\\\Rightarrow \dfrac{7}{0.695} = \dfrac{8}{sinR} = \dfrac{10}{sinS}\\\Rightarrow sin R = \dfrac{8 \times 0.695}{7}\\\Rightarrow R = 52.58^\circ

\Rightarrow sin S = \dfrac{10 \times 0.695}{7}\\\Rightarrow S = 83.14^\circ

Smallest angle is \angle T

Correct answer is option A. T

4 0
4 years ago
True or False<br><br> The additive inverse (opposite) of (a2 - 2a + 3) is (-a2 + 2a - 3)
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True.. the “opposite” is just the opposite signs:)
5 0
3 years ago
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topjm [15]
The answer is B because the bottom has to be supplementary to 180 degrees because their supplementary angles
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3 years ago
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Tasya [4]
If Hannah gives her younger sister 3 shirts, it does not matter what order she hands them to her. No matter the order, it will still be the same group of 3 shirt. Since order is not important this problem can be solved using a combination. 
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3 0
4 years ago
13. When measuring weight, 100 pounds is equal to 45.3392 kilograms. Round this weight to the nearest hundredth of a kilogram._​
Lostsunrise [7]

Answer: 45.34 kilograms

Step-by-step explanation:

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5 0
2 years ago
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